\relax 
\catcode`"\active
\select@language{ngerman}
\@writefile{toc}{\select@language{ngerman}}
\@writefile{lof}{\select@language{ngerman}}
\@writefile{lot}{\select@language{ngerman}}
\@writefile{toc}{\contentsline {chapter}{\numberline {1}Algebraische und arithmetische Algorithmen}{1}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\@writefile{toc}{\contentsline {section}{\numberline {1.1}Das algebraische Berechnungsmodell}{1}}
\@writefile{toc}{\contentsline {section}{\numberline {1.2}Matrizenmultiplikation}{1}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.2.1}Algorithmus von Strassen (1969)}{1}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.2.2}Ausblick}{3}}
\@writefile{toc}{\contentsline {section}{\numberline {1.3}Inversion und Determinante von Matrizen}{3}}
\@writefile{toc}{\contentsline {section}{\numberline {1.4}Multiplikation Boolscher Matrizen (Fortsetzung 18.04.)}{4}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.4.1}Transitiver Abschluss Boolscher Matrizen}{5}}
\@writefile{toc}{\contentsline {section}{\numberline {1.5}Polynommultiplikation, diskrete Fourier-Transformation}{6}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.5.1}FFT ausf\"uhrlich}{7}}
\@writefile{loa}{\contentsline {algorithm}{\numberline {1}{\ignorespaces FFT(a,n,$\omega $)}}{7}}
\newlabel{faltungssatz}{{3}{8}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.5.2}Bedeutung der Fourier-Transformation}{8}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.5.3}Verbesserter Algorithmus zur Multiplikation von Bin\"arzahlen}{9}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.5.4}Verbesserter Algorithmus zur Division von Bin\"arzahlen}{11}}
\newlabel{fig:Newton-Iteration}{{1.5.4}{12}}
\@writefile{toc}{\contentsline {section}{\numberline {1.6}Berechnung der Quadratwurzel}{13}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.6.1}Schulmethode}{13}}
\@writefile{toc}{\contentsline {subsubsection}{Im Dezimalsystem}{13}}
\@writefile{toc}{\contentsline {subsubsection}{Im Bin\"arsystem}{13}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.6.2}Quadratwurzel mit Newton-Iteration berechnen}{14}}
\@writefile{toc}{\contentsline {subsubsection}{zum Newtonverfahren}{14}}
\@writefile{toc}{\contentsline {section}{\numberline {1.7}Primzahltest}{14}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.7.1}Primzahltest von Miller und Rabin}{15}}
\@writefile{toc}{\contentsline {subsubsection}{Kleiner Satz von Fermat}{15}}
\@writefile{toc}{\contentsline {subsubsection}{Algorithmus (von Miller, Rabin)}{15}}
\@writefile{toc}{\contentsline {subsubsection}{Korrektheit}{15}}
\@writefile{loa}{\contentsline {algorithm}{\numberline {2}{\ignorespaces PrimMillerRabin($N$,$k$)}}{16}}
